length of curve in a metric space

Suppose that (X,d) is a metric space. Let f be a curve, so that f:[0,1]X is a continuous functionMathworldPlanetmathPlanetmath, and let 0=t0<t1<<tn=1 and xi=f(ti) for 0in. The set {x0,x1,,xn} is called a partitionPlanetmathPlanetmath of the curve. The of the curve is defined to be the supremum over all partitions of the quantity i=1nd(xi,xi-1).

Title length of curvePlanetmathPlanetmath in a metric space
Canonical name LengthOfCurveInAMetricSpace
Date of creation 2013-03-22 16:50:27
Last modified on 2013-03-22 16:50:27
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 8
Author Mathprof (13753)
Entry type Definition
Classification msc 26B15
Defines length of a curve